In the present paper a bi-objective integer linear programming problem (BILP) is discussed. The main effort in this work to effectively implement ?-constraint method produce complete set of non dominated points. convergence algorithm has been established theoretically. Further comparative study some existing also made.

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...